When are all modules semichain modules?
Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 173-182.

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A module is called a chain module if the structure of its submodules forms a chain. It is proven that all left $R$-modules can be decomposed into a direct sum of chain modules if and only if the ring $R$ is generalized uniserial.
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     author = {L. A. Skornyakov},
     title = {When are all modules semichain modules?},
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L. A. Skornyakov. When are all modules semichain modules?. Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 173-182. http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a4/